Oates or Depp? Depends what you're looking for.
Milius' "Dillinger" is a great entertainment, and a great work of fiction-- emphasis on fiction. "Public Enemies" will also take quite a few liberties with literal historical truth, but not nearly as many as "Dillinger" does.
More importantly, PE will emphasize the innocent-acting "good boy gone wrong" side of Dillinger's character, whereas Milius' film shows us a tough-as-nails hardened criminal; an elegant and eloquent thug, but a thug nevertheless.
In my estimation, the real John Dillinger was roughly 1/4 to 1/3 of the way between Michael Mann's Dillinger and Milius'.
Still, there's no doubt that Warren Oates turned in a tour de force performance, and so did Ben Johnson as Melvin Purvis. Both were, strictly speaking, too old for their roles, but who cares?
Throw in Harry Dean Stanton, Michelle Phillips, and Richard Dreyfuss, and some really brilliant dialogue in Milius' script, and you've got some great chemistry going in this underrated flick. But obviously, the star-studded cast of "Public Enemies" could turn out just as impressive a showing, or better.
Your pointing out that Depp is about the same age Oates was, in 1973, is the only redundant thing here. It's been said many times before. The point is, Depp doesn't look 45. If anything, he looks younger than Dillinger did at 31.
Oates at 44 looked like he was over 50.
But physical appearance isn't really what's at stake. There was a very different side to John Dillinger's character that Milius didn't even try to touch. Mann will, and if he does a good enough job of directing, Depp certainly has the acting talent to live up to the role-- again, as written.
I don't have a problem with Oates' performance in this film. It's excellent. But it's not John Dillinger.
"I don't deduce, I observe."
IMHO, so far Oates is THE Dillinger. Oates' film had a number of flaws, but he was great. Purvis did not look like Ben Johnson. More like Mr. Peepers.